Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
A common belief is that the law of averages will rule in the long run, eliminating risk.
It’s true that the average outcome from a gamble should not be risky in the long run.
But the gain or loss from gambling is average gain per gamble \(\times\) number of gambles.
Based on history, the bet is definitely in our favor. We have much better odds than in a casino.
If we play for a long time, we will almost certainly come out ahead.
But how far ahead is quite uncertain.
Let’s look at the best and worst periods in the past.
Note the variation in compounded returns in different simulations
Same exercise as in our first module
But generate a random return each month of the investment lifetime
And simulate many lifetimes in this way
If we want to forecast a constant return (not simulate) and base the return on history, should we use the historical arithmetic average or historical geometric average?
Geometric average is better for forecasting future compounded returns.
Arithmetic average is better for forecasting future (arithmetic) average return.